\subsection{M. Combescot's suggestion}
I tried on the the suggestion by M. Combescot \ref{sec:MCombescot}.  The normalization is problemetic.  It is like grand cannonical ensemble of coboson.  You have to sum all the possibility of particle numbers in close-channel state $B^+$ from 0 to $\infty$ to get the quantities such as the normalization, $\av{n}$... 